What good fortune that you have found your way here!
We have codified our knowledge and discoveries on SSRS migrations in a whitepaper that we feel you'll find far more substantive than the average free whitepaper. While not a cookbook, with this guidance you will have taken the first step towards a seamless migration, and we will have introduced ourselves in case you need some assistance along the way.
This whitepaper focuses particularly on native mode and on-premises upgrade from SSRS 2008 R2 to SSRS 2016. However, even if your scenario does not exactly meet this use case, the bulk of the information presented will still be helpful.
Considering the timing of this post, we would be remiss to not mention a current Microsoft promotion involving SQL Server 2008 & 2008 R2 (including SSRS). You may already know that Microsoft's product lifecycle for 2008 R2 is going off Extended Support. That means no more support, or more notably, no more security patches. If you're running SQL Server 2008 & 2008 R2, you can get your company three more years of Extended Support for FREE with no code changes.